Spinozism and Life in the Chaosmos

David Lewis

Whether knowingly drawing from Nietzsche’s claim or not, from Human All-too-Human, which asserts that ‘He who strays from tradition becomes a sacrifice to the extraordinary; he who remains in tradition is its slave. Destruction follows in any case’, David Lewis’s advice to his then graduate student, Robert Brandom, was that to carry the tradition forward one needed to go back to tradition, and more precisely to its first principles. To jump forward one needs to back up and get a running start (and somewhere Nietzsche says much the same thing though I can’t find the quote)–hence, ‘reculer pour mieux sauter.’ As Brandom summarizes Lewis’s advice, he claims that

The way to understand some region of pure philosophical terrain is for each investigator to state a set of principles as clearly as she could, and then rigorously to determine what follows from them, what they rule out, and how one might argue for or against them. (Tales of the Mighty Dead, 114-15).

If I am going to understand Spinoza, Leibniz, Hume, or Deleuze; or the Federalist Papers, the pragmatists, and perhaps even analytic philosophy more generally; the key in each case is to determine the guiding, predetermining principles that can account for what is said. This is how Brandom seeks to balance the de dicto and de re readings of the philosophical tradition. The de dicto readings are to be limited in their interpretations only to what a particular author is committed to as is evidenced by what they have written, and more generally to what they have read and to the problems and concerns of their intellectual milieux. The de re readings base interpretations upon what are taken to be true principles and facts that may or may not be acknowledged by a de dicto reading of a given text. Once one has backed up and found the principle or set of principles that best accounts for much of what can be found within the works of a given philosopher or a certain ‘philosophical terrain’, one then deduces the conclusions that follow from these principles, regardless of whether or not the actual, de dicto conclusions one actually finds in the texts are in line with these conclusions or not. Brandom’s historical essays in The Tales of the Mighty Dead are quite faithful to Lewis’s advice, and he applies this methodology to his readings of Spinoza, Leibniz, Hegel, Frege, Heidegger, and Sellars, drawing along the way a number of interesting conclusions. Brandom’s leap into these texts thus involves quite a running start.

As much as I am attracted to Lewis’s advice for doing intellectual history, I find that it is only half the story. First, and most importantly, it seems to me that creative philosophical work does not begin with a set of first principles from which one then deduces their conclusions. Brandom would probably agree with this claim; after all, he refers to his reading of the tradition as an exercise in ‘reconstructive metaphysics’. But the implication nonetheless is that despite the perhaps wanton creative process associated with a philosophical endeavor, there is nonetheless a set of guiding principles that illuminates the true significance of the project, even if only after the fact (as if such principles were the unconscious directives of what is written). Such an approach is integral to identifying the critical moves in a philosophical argument, or in determining the essential relations between key components of one’s thought; however, such identifications only actualize the processes associated with the philosophical developments of a position, and the continuing and ongoing transformations of this/these position(s). What is overlooked, and this is the other half of the story, are the concepts that philosophers create. A philosophical concept cannot be reduced to a predetermining set of principles; moreover, a philosophical concept cannot even avoid giving rise to contradictions, or to intellectual mitosis as was discussed in an earlier post. I may be over-generous, but the Lewisean/Brandomian approach is indeed an important after the fact way to set forth a discursive account of the inferential premises and conclusions of a particular philosophical argument/position, but to become truly creative such an approach needs to encounter problems that resist such a reduction to principles; and for this reason, and others besides, philosophical concepts are not to be confused with first principles.

In his account of necessity David Lewis proposes that given two worlds that are exactly alike at time1, W and W*, and in which the same natural laws apply, then at any later time these two worlds will continue to be exactly alike. As a good Humean, however, Lewis encountered what he claimed to be a damning problem, the problem of undermining futures. On Lewis’s reading of Hume, any claims or truths we make regarding the world, including claims concerning necessary laws, supervene upon a given distribution of qualities. There cannot be a change in this distribution without there also being a change in the claims or truths that supervene upon them. Given the laws of probability, the chances of a dice coming up showing a six is one in six. Three or four sixes may show up in a row, but given a large enough number of throws the number of times it shows up sixes approaches one in six. These laws of probability therefore supervene upon a given distribution of qualities in the world up to and including time1. If there is a non-zero chance, however, that after time1 sixes come up every time then that would effect the chance distribution at W at time1—it would be something higher than one in six, but this contradicts Humean supervenience. Given the case of an undermining future we would assign a probability value x and non-x to the throw of the dice at time1. In his response to this problem, Lewis proposes modifying the laws, but many have been unhappy with Lewis’s proposal. In his analysis of Hume in After Finitude, Meillassoux, following Badiou, would argue that the very laws themselves presuppose a totalized whole, an All, in order for there to be the regularities upon which these necessary laws supervene. If mathematics thinks the not-All, however, then there is no reason why Humean supervenience needs to stay the same or be different at a later time. The notion of an undermining future would be vacated of sense. We may continue to axiomatize and mathematize the distribution of qualities in the world, but there is no All which assures their necessity, and hence no necessity to be undermined. The only necessity for Meillassoux is the necessity of contingency. In his response to the problem of undermining futures, John Roberts argues that what gives rise to the problem is the idealization of our knowledge of chance at time1. It is only under the assumption that we can specify a particular value to the chance of a particular event happening whereby we are led to a contradictory belief when the undermining future entails a different value and result. ‘But real evidence,’ Roberts claims, ‘never constrains these credences by specifying the objective chances of such events.’ (“Undermining Undermined,” p. 104) As Roberts clarifies, ‘if HS is correct, there could be such evidence only if there were no problem of induction,’ meaning that this evidence would have to ‘entail…contingent information about the future, something no evidence in principle available to creatures like us could ever do.’ (ibid.). By constraining evidence concerning chance and supervenience to ‘finite empirical cognizers,’ Roberts is able to block the reduction that results from undermining futures. In other words, people like us, finite cognizers, are simply unable to process all the evidence necessary to get the appropriate value, much less the undermining futures which we cannot even access, and thus we would be unable to generate the contradictory value. In doing this, however, Roberts fails to avoid the central critique of Meillassoux’s book. By calling upon the mathematical thinking of the not-All associated with Cantorian set-theory, Meillassoux sought to address the correlationist trap that has been in place since Kant—namely, we cannot know an object as it is in itself except for how it appears in its relationship to us as finite empirical cognizers. This is precisely what Roberts does, however, and the fact that Lewis himself was not attracted to the solution Roberts offers should give us pause. The reason for this is that Lewis sought, with the tools of modal logic, to do much what Meillassoux and Badiou would like to do—break free from the limiting cages of finite cognizers and arrive at truths about an autonomous reality that is not correlated to a finite cognizer. As a good Humean, however, Lewis would no doubt not accept Meillassoux’s rejection of the problem of undermining futures, the problem of induction, and similarly Meillassoux would reject Lewis’s approach since Humean supervenience continues the correlationsist legacy—knowledge of reality in itself is correlated to the various qualities of the world as they are related to a presupposed totality. This last claim I think is debatable since Lewis’s metaphysics may well involve a reality of possible worlds that are non-totalizable. Lewis nonetheless continued to believe in the necessity of natural law, thus even if there is a transfinite set of possible worlds (a not-All), the laws, whatever they are in each world, would hold as a consequence of the totality of that world; and hence Meillassoux’s argument would resurface.

At this point we can turn to Deleuze’s understanding of mathematics to clarify our take on Lewis’s position. As Daniel Smith has shown in his essay on the importance of mathematics in understanding Deleuze’s theory of multiplicities, and how this theory in turn differs from Badiou’s theory of the multiple-without-One, Smith shows that Deleuze’s theory is informed by a tradition of problematics in mathematics in contrast to the axiomatic approach favored by Badiou. (“Mathematics and the Theory of Multiplicities”). The difference becomes clear in Deleuze and Guattari’s very definition of the nondenumerable: ‘What characterizes the nondenumerable is neither the set nor its elements; rather, it is the connection, the “and” produced between elements, between sets, and which belongs to neither, which eludes them and constitutes a line of flight.’ (TP 518). The nondenumerable is problematic, for Deleuze, precisely because it constitutes problems that have, as Smith puts it, ‘an objectively determined structure, apart from its solution,’ and this objectively determined structure entails ‘a zone of objective indetermination’ that precludes being reduced to demonstrative and axiomatic methods in mathematics. The ‘genetic and problematic aspect of mathematics…remains inaccessible to set theoretical axiomatics,’ and yet, through continual movements and translations, the problematic in mathematics gives way to axiomatic innovations and recodings (Smith offers the example of the translation of infinitesimals and approaching the limit in calculus [an example of the problematics tradition] into the axiomatic epsilon-delta method as developed by Weierstrass). We have in short what you might call Deleuzian supervenience, whereby the discretization of the axiomatic maps or supervenes upon the continuity of the problematic, but the problematic forever exceeds the axiomatic, it is the ‘power of the continuum, tied to the axiomatic but exceeding it.’ (ibid. 466). Axiomatics, or what Deleuze will also call major or royal science, thus draws from problematics the necessity of inventing and innovating in response to the ‘objectively determined structure’ of the problem. Similarly problematics, minor or nomad science, calls upon axiomatics to actualize the solutions it lays out, if only indeterminately so. Deleuze and Guattari are clear on this point: ‘Major science has a perpetual need for the inspiration of the minor; but the minor would be nothing if it did not confront and conform to the highest scientific requirements.’ (ibid. 486). We can thus rethink Lewis’ problem of induction not as a problem intrinsic to the relationship between a finite cognizer and the distribution of qualities as they relate to this cognizer, but rather as an ‘objectively determined’ problem that exceeds the tools of modal realism and axiomatic logic. Lewis, in short, is encountering the necessity and insufficiency of invention. In the next post we’ll see that one interpretation of why Spinoza abandoned his Treatise on the Emendation of the Intellect was precisely because he, like Lewis, encountered the necessity and insufficiency of invention.